A truth table is a mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments.
Symbols
- Negation ( or ~): Not P
- Conjunction ( or &): P and Q
- Disjunction ( or v): P or Q
- Implication (): If P then Q
- Biconditional (): P if and only if Q
Basic Tables
Conjunction (AND)
True only if both premises are true.
| P | Q | P Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Disjunction (OR)
True if at least one premise is true.
| P | Q | P Q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Implication (Conditional)
False only if P is True and Q is False.
| P | Q | P Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |